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Proofgold Asset
asset id
132e9a243727bdd100428e1bfd6b337444540eba3bb101a0bb5c74b21ea4fdd9
asset hash
85f0521364d605b4b574490ffcbcc09cdd6616f2cc83d9d72318cd562bfff057
bday / block
35140
tx
97617..
preasset
doc published by
PrPhD..
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Theorem
ee513..
:
∀ x0 :
ι →
ι → ο
.
∀ x1 :
ι → ι
.
∀ x2 x3 :
ι →
ι → ο
.
∀ x4 x5 .
∀ x6 :
ι → ο
.
∀ x7 .
∀ x8 :
ι → ο
.
∀ x9 .
∀ x10 x11 :
ι → ο
.
∀ x12 .
∀ x13 :
ι → ο
.
∀ x14 :
ι → ι
.
∀ x15 :
ι → ο
.
∀ x16 .
∀ x17 x18 :
ι → ο
.
∀ x19 .
∀ x20 :
ι → ο
.
∀ x21 x22 x23 .
∀ x24 :
ι → ι
.
∀ x25 x26 :
ι →
ι → ι
.
∀ x27 x28 x29 x30 x31 :
ι → ο
.
∀ x32 .
∀ x33 x34 x35 :
ι → ο
.
∀ x36 :
ι →
ι →
ι → ι
.
∀ x37 :
ι → ο
.
∀ x38 :
ι →
ι → ι
.
∀ x39 .
∀ x40 :
ι → ι
.
∀ x41 .
∀ x42 :
ι → ι
.
∀ x43 :
ι → ο
.
∀ x44 .
∀ x45 :
ι → ι
.
∀ x46 :
ι →
ι → ο
.
∀ x47 :
ι → ο
.
∀ x48 .
∀ x49 :
ι →
ι → ο
.
∀ x50 :
ι → ι
.
∀ x51 :
ι → ο
.
∀ x52 x53 :
ι → ι
.
∀ x54 :
ι → ο
.
∀ x55 .
∀ x56 :
ι → ο
.
∀ x57 .
∀ x58 :
ι → ο
.
∀ x59 .
∀ x60 :
ι → ο
.
(
∀ x61 x62 .
x60
x62
⟶
(
x62
=
x61
⟶
False
)
⟶
x60
x61
⟶
False
)
⟶
(
∀ x61 x62 .
x0
x61
x62
⟶
x60
x62
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x61
=
x59
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x0
x61
x62
⟶
x2
x62
(
x1
x63
)
⟶
x60
x63
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x0
x62
x63
⟶
x2
x63
(
x1
x61
)
⟶
(
x2
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x3
x62
x61
⟶
(
x2
x62
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x61
)
⟶
(
x3
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x61
x62
⟶
(
x60
x62
⟶
False
)
⟶
(
x0
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x0
x62
x61
⟶
(
x2
x62
x61
⟶
False
)
⟶
False
)
⟶
(
(
x2
x59
x4
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x3
x61
x61
⟶
False
)
⟶
False
)
⟶
(
(
x5
=
x4
⟶
False
)
⟶
False
)
⟶
(
(
x58
x57
⟶
False
)
⟶
False
)
⟶
(
x60
x57
⟶
False
)
⟶
(
(
x56
x55
⟶
False
)
⟶
False
)
⟶
(
x60
x55
⟶
False
)
⟶
(
∀ x61 .
(
x54
x61
⟶
False
)
⟶
x54
(
x53
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x54
x61
⟶
False
)
⟶
(
x2
(
x53
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
(
x54
(
x52
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
x60
(
x52
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
(
x2
(
x52
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
(
x6
x7
⟶
False
)
⟶
False
)
⟶
(
x60
x7
⟶
False
)
⟶
(
x8
x9
⟶
False
)
⟶
(
(
x51
x9
⟶
False
)
⟶
False
)
⟶
(
(
x10
x9
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
(
x49
(
x50
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
(
x2
(
x50
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
(
x6
x48
⟶
False
)
⟶
False
)
⟶
(
(
x11
x12
⟶
False
)
⟶
False
)
⟶
(
(
x47
x12
⟶
False
)
⟶
False
)
⟶
(
(
x13
x12
⟶
False
)
⟶
False
)
⟶
(
x60
x12
⟶
False
)
⟶
(
(
x51
x12
⟶
False
)
⟶
False
)
⟶
(
(
x46
x12
x5
⟶
False
)
⟶
False
)
⟶
(
(
x10
x12
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x49
(
x45
x61
)
x61
⟶
False
)
⟶
(
∀ x61 .
(
x2
(
x45
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
(
x11
x44
⟶
False
)
⟶
False
)
⟶
(
(
x51
x44
⟶
False
)
⟶
False
)
⟶
(
(
x10
x44
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
(
x14
x61
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x2
(
x14
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
(
x15
x16
⟶
False
)
⟶
False
)
⟶
(
(
x43
x16
⟶
False
)
⟶
False
)
⟶
(
(
x17
x16
⟶
False
)
⟶
False
)
⟶
(
x60
x16
⟶
False
)
⟶
(
(
x18
x19
⟶
False
)
⟶
False
)
⟶
(
(
x51
x19
⟶
False
)
⟶
False
)
⟶
(
(
x10
x19
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
x60
(
x42
x61
)
⟶
False
)
⟶
(
∀ x61 .
(
x60
x61
⟶
False
)
⟶
(
x2
(
x42
x61
)
(
x1
x61
)
⟶
False
)
⟶
False
)
⟶
(
(
x15
x41
⟶
False
)
⟶
False
)
⟶
(
(
x20
x21
⟶
False
)
⟶
False
)
⟶
(
x60
x21
⟶
False
)
⟶
(
(
x51
x22
⟶
False
)
⟶
False
)
⟶
(
(
x10
x22
⟶
False
)
⟶
False
)
⟶
(
(
x15
x4
⟶
False
)
⟶
False
)
⟶
(
x60
x4
⟶
False
)
⟶
(
(
x56
x23
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
(
x1
x61
)
⟶
False
)
⟶
(
(
x20
x23
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
(
x2
(
x40
x61
)
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x2
x61
(
x1
x23
)
⟶
(
x2
(
x24
x61
)
(
x1
x23
)
⟶
False
)
⟶
False
)
⟶
(
(
x2
x5
(
x1
x39
)
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x0
(
x25
x61
x62
)
x61
⟶
(
x3
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x0
(
x25
x61
x62
)
x62
⟶
False
)
⟶
(
x3
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x3
x62
x63
⟶
x0
x61
x62
⟶
(
x0
x61
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x2
x63
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x2
x62
(
x1
x23
)
⟶
x37
x62
⟶
x3
x63
x62
⟶
(
x0
(
x38
x61
x63
)
x62
⟶
False
)
⟶
(
x0
(
x38
x61
x63
)
x61
⟶
False
)
⟶
(
x61
=
x24
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x0
(
x38
x61
x62
)
x61
⟶
x0
(
x38
x61
x62
)
(
x26
x61
x62
)
⟶
(
x61
=
x24
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x0
(
x38
x61
x62
)
x61
⟶
(
x3
x62
(
x26
x61
x62
)
⟶
False
)
⟶
(
x61
=
x24
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x0
(
x38
x61
x62
)
x61
⟶
(
x37
(
x26
x61
x62
)
⟶
False
)
⟶
(
x61
=
x24
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x0
(
x38
x61
x62
)
x61
⟶
(
x2
(
x26
x61
x62
)
(
x1
x23
)
⟶
False
)
⟶
(
x61
=
x24
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x2
x62
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
(
x2
(
x38
x61
x62
)
x23
⟶
False
)
⟶
(
x61
=
x24
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x2
x63
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x61
=
x24
x63
⟶
x2
x62
x23
⟶
x0
x62
(
x36
x62
x61
x63
)
⟶
(
x0
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x2
x63
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x61
=
x24
x63
⟶
x2
x62
x23
⟶
(
x3
x63
(
x36
x62
x61
x63
)
⟶
False
)
⟶
(
x0
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x2
x63
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x61
=
x24
x63
⟶
x2
x62
x23
⟶
(
x37
(
x36
x62
x61
x63
)
⟶
False
)
⟶
(
x0
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 .
x2
x63
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x61
=
x24
x63
⟶
x2
x62
x23
⟶
(
x2
(
x36
x62
x61
x63
)
(
x1
x23
)
⟶
False
)
⟶
(
x0
x62
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 x63 x64 .
x2
x64
(
x1
x23
)
⟶
x2
x61
(
x1
x23
)
⟶
x61
=
x24
x64
⟶
x2
x62
x23
⟶
x0
x62
x61
⟶
x2
x63
(
x1
x23
)
⟶
x37
x63
⟶
x3
x64
x63
⟶
(
x0
x62
x63
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x27
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x56
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x56
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x58
x61
⟶
(
x56
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x2
x61
x4
⟶
(
x6
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x56
x62
⟶
x2
x61
x62
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x56
x62
⟶
x2
x61
x62
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x58
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x6
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x56
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x11
x61
⟶
(
x11
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x11
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x11
x61
⟶
(
x46
x61
x5
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x11
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x6
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x54
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x8
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x54
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x54
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x11
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x54
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x54
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x15
x62
⟶
x2
x61
x62
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
(
x8
x61
⟶
False
)
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
(
x8
x61
⟶
False
)
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
(
x8
x61
⟶
False
)
⟶
x54
x61
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x47
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x46
x61
x5
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x60
x62
⟶
x2
x61
(
x1
x62
)
⟶
x49
x61
x62
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x28
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x8
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x60
x61
⟶
(
x47
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x60
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
x2
x61
(
x1
x62
)
⟶
x60
x61
⟶
(
x49
x61
x62
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x2
x61
x23
⟶
(
x47
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x10
x62
⟶
x51
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
(
x60
x62
⟶
False
)
⟶
x2
x61
(
x1
x62
)
⟶
(
x49
x61
x62
⟶
False
)
⟶
x60
x61
⟶
False
)
⟶
(
∀ x61 .
x17
x61
⟶
x43
x61
⟶
(
x15
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x18
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
x10
x61
⟶
x51
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x13
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x51
x61
⟶
x47
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x60
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x60
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x15
x61
⟶
(
x43
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x15
x61
⟶
(
x17
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x35
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x29
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x34
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x30
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x33
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
(
x31
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x20
x61
⟶
x60
x61
⟶
False
)
⟶
(
∀ x61 .
x60
x61
⟶
(
x51
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x60
x61
⟶
(
x47
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 .
x10
x61
⟶
x60
x61
⟶
(
x10
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x58
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x58
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x27
x62
⟶
x2
x61
(
x1
x62
)
⟶
(
x27
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x58
x62
⟶
x2
x61
x62
⟶
(
x47
x61
⟶
False
)
⟶
False
)
⟶
(
∀ x61 x62 .
x0
x61
x62
⟶
x0
x62
x61
⟶
False
)
⟶
(
x3
x32
(
x24
x32
)
⟶
False
)
⟶
(
(
x2
x32
(
x1
x23
)
⟶
False
)
⟶
False
)
⟶
False
(proof)